Weeknotes #2: Nature of Order Reading Seminar — 15 October 2020
Notes on the Nature of Order Seminar series — part of the Building Beauty Post-Graduate Diploma in Architecture. A weekly running reflection for myself, for friends, and for those curious about Christopher Alexander’s work and its importance in shaping a healthy, living world.
- Ideas presented here build on those introduced in Weeknotes #1
October 15, 2020. It is the 2nd seminar, in which:
- We have read The Phenomenon of Life, pages 143–194, on the first 8 of Alexander’s Fifteen Fundamental Properties of Wholeness
- Yodan presents a short overview of the first 8 properties, what they are, and how they work together in creating living structure
- The seminar discuss the idea of top-down order vs. locally experienced order, and the Nolli plan of Rome
- We reflect on analyzing the properties (and space) through images
- And we are reminded that it’s not so easy to find these properties in the world, but even more difficult to bring forth the living structure that exhibits them…
The Fifteen Fundamental Properties
Alexander describes fifteen properties as repeatedly recurring phenomena, geometrical features, that are common to those spaces and situations which bring forth life from wholeness.
Properties of Wholeness
A child plays with a small puppy in the yard. A woman climbs the steps of Montmartre in the misty rain; at Sacre-Coeur she surveys the sprawl of Paris below, breathless as gentle harp notes slide through the fog. A group of friends stand (with shoes off) on a wooden ledge over the Zen garden of Ryōan-ji — no words, but understanding passes between them. In Pittsburgh, Pennsylvania, a father teaches his daughter to ride her first bicycle in the private alleyway connecting the neighbors’ houses. You sit in a nicely cushioned window alcove at a nearby cafe, morning sunlight streaming down, a mug of hot coffee coffee cooling in your hands…
There are places and situations where the structure of the world causes us to feel alive, because the structure and fabric of the world itself, is whole and alive. If we allow ourselves to take this idea of wholeness and life seriously, if we believe that the structure of the world has life that we can connect with, then we have a basis for investigation of the common properties of living structure. For Alexander’s “Fifteen Fundamental Properties.”
The method by which they come about is remarkable. I will paraphrase page 144:
I asked myself: can we find any structural features which tend to be present in the examples which have more life, and tend to be missing in the ones which have less life? For 20 years, I spent two to three hours a day looking at pairs of things — buildings, tiles, stones, windows, carpets, furniture, streets, doorways, arches — comparing them and asking myself, Which one has more life? And then asking, What are the common features of the examples that have most life? I managed to identify fifteen structural features which appear again and again in things which do have life.
About Centers, and Relationships
We are building now on top of the already established ground of wholeness, life, and beauty. On the theory of centers. The idea of properties that describe living structure are not separate from this prior thinking, but emerge from it. As described here, these are properties that describe how centers work together to produce life in a given scope of the structural fabric we inhabit, the wholeness.
These properties cannot exist independently of centers. And because they refer to the field of centers, an interconnected whole, they also rarely exist in isolation. In examples with abundant life, we are bound to see fields of centers that exhibit many of the properties working together. Rather than “ticking off” the presence or absence of a property, we must consider what it means for different centers to relate to one another in this way, as indicated by a given property.
The First Eight Properties
Yodan begins with a short presentation that describes the eight properties, and he presents none of them alone, but rather presents examples of objects and built environments that present some set of the properties working in concert.
In seminar, we discuss the first eight of these Fifteen Fundamental Properties of Wholeness. Here, I interpret those eight properties based on the discussion, my own interpretation of the reading, and through examples with a few small studies of specific centers. We’ll begin sequentially:
1. Levels of Scale
The first property is introduced Levels of Scale. It indicates that indeed, centers in a living whole have different levels of scale, but also discusses the degree of variation in those scales.
It concerns the degree to which centers help each other, how smaller centers can contribute to the larger centers they are in or around. Life is more intense in a center when the centers near/within it have a definite size relation to it: usually between half its size to two or three times as large its size.
This property works relationally, across different systems of centers within a larger whole, and in recursive composition, in the smaller centers that constitute and create a larger whole; or inversely, in decomposing the larger centers that unify and bind systems of smaller centers.
Here is a simple example from a building nearby, whose centers exhibit a simple and natural scale relationship within their constituent parts, and between the major centers that constitute the entire whole of the building
2. Strong Centers
Given that we are working with the idea of a world constructed from a field of interlocking and overlapping centers, it seems obvious to include ‘Strong Centers’ as a property of life in structure. This property indicates that it’s not enough to see the elements or blobs of space as centers: that life comes from the strength, well-formed-ness of each center. I remind myself to think of ‘Strong centers [of attention]’ to underscore what a center is and how it can function in space.
What brings space alive, what we see repeatedly in positive examples of life, is that there exist some strong centers of attention. A focus, an amplifying center or set of centers, that help to bind together the whole.
In the example, we see that those same centers that are composed of a natural level of scale, are strong and lively as centers encapsulating the whole.
A more striking example of strong centers: the medallions of the carpet below. These centers radiate a living force in their own right, and bring together the entire field of the carpet.
3. Boundaries
The third property, Boundaries, describes a way some centers can focus attention and help produce other centers. They separate centers from, and also unite centers with, the field beyond the boundary.
We can’t take a boundary to act in isolation, as just a boundary-thing: successful boundaries themselves are, and are formed of, centers. A good boundary exists at the same level of magnitude as the center being bounded.
Observe how the window boundaries serve two functions in this facade in Porto. They amplify and bring life to the windows they bound, but they also enhance and connect those windows into the field of tiles outside of the boundaries. The windows are a nice example, as they are bounded in their relationship to the wall, and they are also centers of the boundary between room and street.
If we return to the carpet above, we can see a striking display of how the boundaries frame, amplify, give strength to the primary centers — the medallions of this carpet. And the boundaries themselves are beautiful structures. They are also bounded, by boundaries, which are again strong centers and are themselves bounded one layer deeper.
4. Alternating Repetition
The fourth property, Alternating Repetition, speaks to the rhythm and interplay between multiple systems of centers. Life will not emerge from the banal repetition of one element, but the interplay and oscillation whereby alternating systems of centers strengthen and enhance each other.
Alexander cites the chintamani design in 15th century Turkish velvet as a “waving alternation of color [that] creates a passionate life in the space” (p.165). The life is not, primarily, the alternation between the circles and waves, but an alternation in figure and ground. Examine the the grounding field of deep red as figure — view each red space as a center in its own right — and evaluate how this system of [deep red] positive spaces alternates and repeats with the [light] circles and waves taken as the other system of centers. A remarkable configuration of space, we can almost feel it breathe.
We can find this same type of life generated in a cloister arcade. The columns themselves are a system of strong centers (with good shape, with strong boundaries, with humane levels of scale), and their presence creates a new system of strong centers — the space beneath each arch.
The space is not an object, however it is a clearly identifiable center, with power and good shape, a positive space that seems almost purposefully carved out from a continuous field of column-wall. The life in this cloister arcade comes from a vibrant oscillation, an inseparable alternating repetition between these two systems of centers.
5. Positive Space
In a field of centers exhibiting this fifth property, Positive Space, every bit of space is substantial, it “swells outward,” it is geometrically and spatially positive. Nothing feels left over. Alexander describes positive space where the centers grow together like the kernels of corn on a cob, staying coherent, packing together, adjusting themselves each to the adjustment of the other kernels around them.
This property tends to describe a relationship between adjacent or collocated centers in a similar order of magnitude, or how centers of a lower order interact with the whole that binds them together.
It’s simpler to describe this property this in two dimensional terms. A rule might be, don’t work the figure for the sake of the ground — they must co-evolve. Alexander uses Matisse cutouts as a prime example, where each individual element is positive , the cut paper and the space in between, each shape with an elegance that allows it to succeed as a center.
Here in Porto, we see a simple example of positive space in the facade of the building also referenced above. It’s a simple illustration of how one property, the system of centers forming the boundaries, interacts with another, the positive space generated in the tile wall.
The feeling of life is much more intense when we find this property working spatially, in three dimensions. The cloister example above is a lovely and vibrant positive space. Mentally reverse the “figure” and “ground”: imagine the columns/arches/building to be empty space and the cloister arcade space within and around it to be solid stone… We find this cloister-space, this center, is positive and beautiful in its own right. Again, it feels as if the usable space was beautifully carved, positively generated, from a solid block of stone.
6. Good Shape
Slightly more difficult is the sixth property, Good Shape. It speaks to a seemingly ineffable quality of beauty and simplicity that expresses itself in the overall effect of a field of centers. What is common, though, among centers with Good Shape is that they are themselves composed of centers that are simple, powerful centers, often built from fairly basic geometric pieces.
Even the most complex structures, when they are alive and exhibit good shape, are built from simpler centers and fairly elementary centers. Generally, we can view Good Shape as a property that describes a whole center and operates recursively downward on the centers it comprises.
Alexander gives a simple illustration of a teapot stand (pg. 181): its good shape is shown to come from a set of constituent centers — none complex — that are well shaped in their own right.
A similar example on a larger scale: the castle at Odawara exhibits a good shape in its elegant and cascading form. While it is a complex structure, the centers that compose it are all themselves fairly simple and elementary. No tortuous curves or baseless form-bending are required to build up to the strength of this whole.
Of the first eight, I find this property the most intuitive and the most difficult to bound and characterize without a breadth of examples. Within the reading, examples do provide a coherent sense of what creates good shape. And yet, it remains difficult; it gets the closest of any property to singularly encapsulating the idea of ‘beauty.’ If we ask ourselves, of a structure, an object, a geometry, “is it beautiful?” and can deeply and honestly answer “yes,” it’s likely we’re dealing with Good Shape.
7. Local Symmetries
Here is a very particular and interesting property that contains a key to understanding the larger configuration of wholeness-as-unifying-structure.
The idea of local symmetry is entirely different from that of global symmetry. Within this distinction we can find and discuss the idea of an adaptive architecture built of local symmetry from the bottom up, versus a totalitarian architecture imposing its global symmetry onto the world from the top down.
Alexander discusses the Alhambra, in plan, as a prime example of local symmetry. On the whole it is “wildly asymmetrical,” and yet, at any local point, we find a clear abundance of symmetrical elements. Rather than a global order of symmetry, larger centers and elements can unfold in a manner adaptive to the other centers around, and maintain a local coherence in their symmetry at a smaller scale.
Local symmetries can exist within and across multiple centers at similar and different levels of scale. It is not just that a subunit is symmetrical within itself, along some axis. It is also that the subunit and another may share a local symmetry along an entirely different axis. Through different scales and scopes of local symmetry, centers are bound together, “glued” together in how they are felt, at multiple levels.
A philosophical distinction in local vs. global symmetry can also be examined through Alexander’s discussion of the mathematical structure of wholeness in his short essay “A City is Not a Tree.” (This is the essay that signified his rejection of the mathematical decomposition of a design problem as presented in Notes on the Synthesis of Form.)
8. Deep Interlock and Ambiguity
Our final property for the day, Deep Interlock and Ambiguity, speaks to the feeling in living structure that centers are “hooked” into their surrounding centers. Perhaps literally, in design motifs like the traditional meander or Greek key design, and at other times through the ambiguity of the space between them. It is a property that refers to how centers is enmesh in their surroundings.
In structures that are alive, we see this property when two centers, seemingly separate, interact with one another or “grip” each other in such a way as to provide clear interlock or ambiguity — in either case there is some zone between multiple centers where their self-contained-ness breaks down. If that zone is particularly well formed, and a healthy center in its own right, we may also be looking at a Boundary.
In seminar, Yodan presents an example of the bench built by a prior class of Building Beauty students.
The bench itself is a simple center, and deeply locked into the centers around it. One path leads directly into the bench, and is terminated by the shape of the bench. Another path crosses in front of the bench and interacts with that same small enclosure. Sitting on the bench, one is a spot to see the sea below from within the garden, binding the garden and its external view togther. The bench is not globally symmetrical (but does contain strong portions of local symmetry) so that it can accommodate and interact with the branches of the garden to its right. Here we see an example of the property in the sense of ambiguous than hooked interlock. Especially to its right, as we view it , where does the bench end, and the garden wall begin?
In the more literal sense, and in a prime Alexander-style example, we find wonderful and vibrant interlock of the centers in the field of this Lotto carpet. Life springs from the relationship between them, centers and systems of centers that are hooking, pushing, grabbing, pulling, surrounding, and enfolding each other. The geometry is remarkable; try sketching out how this pattern works and the intensity of the interlock and overlap will become immediately apparent.
A final carpet bonus: strong boundary centers with boundaries of their own, alternating repetition, remarkable positive space, and complex overlapping local symmetries all help bring this weaving to life…
Please remember; it’s not that these properties “exist” in the carpet, rather, we can use these properties to describe how the centers in the carpet work together to make it more whole, more beautiful, and more alive.
Top Down vs. Experienced Order
After an introduction to these 8 properties, we discuss the examples including 3 works of Narendra’s art—each could be interpreted to express the nature of city, in differing degrees of abstraction. One was especially reminiscent of the Nolli plan, which we also discuss.
Properties in Plan
The Nolli plan was one of the first measured maps of a city, which uses a horizontal projection that we now take for granted. The map does not just present space in white and buildings in in grey, but rather it shows public spaces in white and private spaces shaded in grey. You’ll note that the interior of churches are visible as public space.
In the portion of the map seen here, on the whole, we will not judge it to be “symmetrical.” However, as we move more deeply down the levels of scale, into its specific subunits, and their subunits, we find an abundance of local symmetries that overlap and bind together various centers of space. We see a healthy relationship in levels of scale of the major centers, and some deep interlock public and private spaces. Generally positive space throughout—nowhere left over, no discarded space. There is lively organic quality in the space depicted in this map.
There is a stark difference of character seen in the Rome of Nolli plan versus a high modernist project like Pruitt–Igoe (an admittedly easy project to pick on), which contains few if any of the first eight properties we’ve discussed. Why such a difference, how can one feel so alive, and one feel so stark?
It comes down to which perspective is most valued during the process of creation—the system of production that produces the place. When we see examples of the 15 properties in plan, feel a healthy living character, it is manifest on the ground. Formal overhead symmetry in plan is an imposition, a disregard for the local perspective, privileging the planner or the architect’s ideas of formal coherence. (I first encountered a broad perspective of the high modernist phenomenon and top down “administrative legibility” in James C. Scott’s “Seeing Like a State,” which makes a strong case for Alexander’s approach by showing how its opposite destroys local adaptation and life on the ground.)
We don’t experience architecture from thee aeroplane, we live with it, and in it, on the ground. What may be messy in plan is where a person can view thousands of local symmetries, that are wonderfully coherent and whole, but will not show up as simplistic overhead symmetry.
Properties as Shackles?
The question was raised in the seminar about creative freedom, about whether or not we restrict ourselves if we take some set of properties as the arbiter of life.
Do we lose spontaneity and life if we try to build with the 15 properties as our guide?
No, and it’s because our aim as builders is not to create the Fifteen Properties or be bound by them. It is to once again create space and places in the world where we feel whole, alive, and at one with ourselves and our communities.
It is Alexander’s conjecture that, when we do this successfully, the Fifteen Properties unfold. They emerge from the living structure because they are foundational set of relationships that allows space to live. We can, perhaps, use them as a suggestion for exploration, but (as we will come to learn in Volume II) any process that does not adapt step by step to its users and its conditions, any process that is rigidly governed by image or by pre-conceived notion, will not be able to produce life. These properties, these relationships between centers, are the geometric symptoms of life.
Closing: Evaluating Properties + Drawing Beauty
Yodan brings the session to a close with two practical exercises. For those of us in this course, the most basic tool at our disposal is still a personal sensitivity to, and understanding of, the life in the structure around us.
How difficult, or how easy is it, to find strong living examples exhibiting these first properties? I think it is quite difficult. To find those things that have a strong complexity and compactness and many of them working together? It is hard to do. And to build it—to make living structure is an even larger task… So start with these exercises:
(1) Take something that you really like, a picture, an image, a work of art, or an object, and analyze its centers. Be true to yourself, not mechanistic in your interpretation; it’s not a checklist of “Do I have positive spaces? Do I have levels of scale?” You have to feel the centers first — they really have to be there—and then look for these properties in how the centers work together.
(2) Draw, and set your mind to create something beautiful. Start with one property as a guide, with positive space (for example.) You’ll find that in order to create positive space, you end up weaving in a lot of the other properties. Start to see what it takes to make something that feels whole. Most of all, be very truthful about whether you’re successful or not—if your use of that property brings out life. Hang it on the wall, look at it for a few hours, see if it still is satisfying. Look at it for a few days. Look at it for a week. If after a week you still want to see it, then perhaps it’s something that has life in it.
And that’s week 2 in the books. See you next week, for the next 7 properties.
Thanks to Building Beauty for creating the Nature of Order reading seminar, and keeping it a free and publicly accessible part of the program.
Whether or not you’re a builder, if you feel a spark in the above, I can only recommend you find your way to a copy of the Nature of Order. It’s a remarkable work.
